Information on Result #735886
Linear OA(25664, 65804, F256, 25) (dual of [65804, 65740, 26]-code), using (u, u+v)-construction based on
- linear OA(25614, 262, F256, 12) (dual of [262, 248, 13]-code), using
- construction X applied to AG(F, Q+80P) ⊂ AG(F, Q+81P) [i] based on
- linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using algebraic-geometric code AG(F,122P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using algebraic-geometric code AG(F, Q+122P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2562, 5, F256, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to AG(F, Q+80P) ⊂ AG(F, Q+81P) [i] based on
- linear OA(25650, 65542, F256, 25) (dual of [65542, 65492, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25664, 32902, F256, 2, 25) (dual of [(32902, 2), 65740, 26]-NRT-code) | [i] | OOA Folding | |